Question

Function with some partition such that $\underline{S}(f,P) = \overline{S}(f,P)$ implies that $f$ is constant

score 26 · Answer 1 · 2021-10-27 23:47:27

26

Views

Function with some partition such that $\underline{S}(f,P) = \overline{S}(f,P)$ implies that $f$ is constant

Published on 27 Oct 2021 - 23:47

score 41 · Answer 2 · 2021-11-03 09:38:52

41

Views

Example for partition $ \prod = \{ x_0 < x_1 < ... < x_n \} $ of $ [a,b] $ where $ \max\{ | x_i - x_{i-1} | : i = 1,...,n \} < \delta $

Published on 03 Nov 2021 - 9:38

score 853 · Answer 3 · 2021-11-27 12:32:34

853

Views

If $f:[a,b]\to\mathbb{R}$ is bounded then $L(f,[a, b])=\lim _{n\to\infty} L(f, P_n,[a, b])$ and $U(f,[a, b])=\lim _{n\to\infty} U(f, P_n,[a, b])$

Published on 27 Nov 2021 - 12:32

score 338 · Answer 4 · 2022-01-04 22:51:08

338

Views

Different ways of constructing a partition of an interval

Published on 04 Jan 2022 - 22:51

score 76 · Answer 5 · 2022-01-16 12:24:25

76

Views

Show that the Rieman integral of $f$ is ...

Published on 16 Jan 2022 - 12:24

score 617 · Answer 6 · 2022-02-01 21:06:14

617

Views

When would we want to use uneven subintervals in a Riemann integral?

Published on 01 Feb 2022 - 21:06

score 231 · Answer 7 · 2022-02-02 02:44:19

231

Views

Prove a function with infinite discontinuous points is Riemann integrable

Published on 02 Feb 2022 - 2:44

score 41 · Answer 8 · 2022-03-09 20:17:08

41

Views

The infimum over all partitions is the same as the infimum over all partitions including a fixed partition $Q$

Published on 09 Mar 2022 - 20:17

score 31 · Answer 9 · 2022-03-23 19:23:02

31

Views

Useful properties for integration

Published on 23 Mar 2022 - 19:23

score 62 · Answer 10 · 2022-04-14 22:24:57

62

Views

How to prove that $g(x)=x^2$ is integrable on $[2,5]$ using regular partitions?

Published on 14 Apr 2022 - 22:24

score 543 · Answer 11 · 2022-04-24 15:37:36

543

Views

Category of partitions of an interval

Published on 24 Apr 2022 - 15:37

score 216 · Answer 12 · 2022-05-17 21:31:01

216

Views

If $S$ is set of lower sums for partitions having $n$-equal subintervals, does $\sup S$ equal the $\sup$ of the set of lower sums for all partitions.

Published on 17 May 2022 - 21:31

score 29 · Answer 13 · 2022-05-30 12:19:17

29

Views

Show $\{n(\int_0^1 f(t)dt- R_n(f)):n\in\mathbb{N}\}$ is bounded

Published on 30 May 2022 - 12:19

score 33 · Answer 14 · 2022-09-03 19:52:54

33

Views

Upper sum infimum of function with property: ∀ε>0 $\exists N \in \mathbb N \cup \{0\}:\lvert\{x\in[a,b]: |d(x)| \gt \varepsilon\} \rvert = N$

Published on 03 Sep 2022 - 19:52

score 36 · Answer 15 · 2022-09-06 16:46:33

36

Views

Partitions in Definite Integral

Published on 06 Sep 2022 - 16:46

List Question

Function with some partition such that $\underline{S}(f,P) = \overline{S}(f,P)$ implies that $f$ is constant

Example for partition $ \prod = \{ x_0 < x_1 < ... < x_n \} $ of $ [a,b] $ where $ \max\{ | x_i - x_{i-1} | : i = 1,...,n \} < \delta $

If $f:[a,b]\to\mathbb{R}$ is bounded then $L(f,[a, b])=\lim _{n\to\infty} L(f, P_n,[a, b])$ and $U(f,[a, b])=\lim _{n\to\infty} U(f, P_n,[a, b])$

Different ways of constructing a partition of an interval

Show that the Rieman integral of $f$ is ...

When would we want to use uneven subintervals in a Riemann integral?

Prove a function with infinite discontinuous points is Riemann integrable

The infimum over all partitions is the same as the infimum over all partitions including a fixed partition $Q$

Useful properties for integration

How to prove that $g(x)=x^2$ is integrable on $[2,5]$ using regular partitions?

Category of partitions of an interval

If $S$ is set of lower sums for partitions having $n$-equal subintervals, does $\sup S$ equal the $\sup$ of the set of lower sums for all partitions.

Show $\{n(\int_0^1 f(t)dt- R_n(f)):n\in\mathbb{N}\}$ is bounded

Upper sum infimum of function with property: ∀ε>0 $\exists N \in \mathbb N \cup \{0\}:\lvert\{x\in[a,b]: |d(x)| \gt \varepsilon\} \rvert = N$

Partitions in Definite Integral

Trending Questions

Popular # Hahtags

Popular Questions